
Regret Matching (RM) [1]}, [2]}. Blackwell's was the the original (external) regret minimization procedure, where each player chooses their next policy proportionally to their positive regrets. [2]} ([2]}) extended their procedure to internal regret by adding a small inertia parameter that causes players to tend to stay in place as their regrets go to 0.

RM+ [5]}. RM+ makes two changes to RM. The first is that a distinction is made between the “true” regrets and the “guiding” regrets, where the guiding regrets are used to determine the policies on the next iteration. After every iteration, any negative guiding regrets are set to zero. The second is that in RM+ iteration \(t\)  is given weight \(t\)  when computing the final average policy (but not when computing the next iteration's policy). RM+ does well with mixed strategies, but does poorly with sampling [6]}.

Linear RM [7]}. Linear RM is identical to vanilla RM except that iteration \(t\)  is given weight \(t\)  (both when computing the average policy and when computing the next iteration's policy).

